Question

A free electron is placed in the path of a plane electromagnetic waves. The electron will start moving

• A. along the direction of electric field.
• B. along the direction of magnetic field.
• C. along the direction of propagation of wave.
• D. in a plane containing the magnetic field and direction of propagation.

Hint:

In problems involving the interaction of EM waves with charges, remember that the force exerted by the electric field component is almost always dominant over the force from the magnetic field component, unless the particle is moving at relativistic speeds.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
An electromagnetic (EM) wave consists of oscillating electric (\(\vec{E}\)) and magnetic (\(\vec{B}\)) fields. These fields are perpendicular to each aother and to the direction of wave propagation. A charge placed in the path of an EM wave will experience forces from both these fields, as described by the Lorentz force equation.

Step 2: Key Formula or Approach:
The total force (Lorentz force) on a charge \(q\) in the presence of electric field \(\vec{E}\) and magnetic field \(\vec{B}\) is: \[ \vec{F} = q\vec{E} + q(\vec{v} \times \vec{B}) \] Here, \(q = -e\) for an electron. The electron is initially free, so we can assume its initial velocity \(\vec{v}\) is zero.

Step 3: Detailed Explanation:
When the free electron is initially placed in the path of the EM wave, its velocity \(\vec{v}\) is zero.
Let's analyze the Lorentz force at this initial moment (\(t=0\)): \[ \vec{F} = (-e)\vec{E} + (-e)(\vec{0} \times \vec{B}) \] \[ \vec{F} = -e\vec{E} \] The magnetic force component is initially zero because the electron is at rest. The only force acting on the electron at the moment it is placed in the wave is the electric force, \(\vec{F}_E = -e\vec{E}\).
This force will cause the electron to accelerate. The direction of this initial acceleration (and hence the initial motion) is opposite to the direction of the electric field \(\vec{E}\) (due to the negative charge). However, since the electric field of an EM wave is oscillating, the force will also be oscillating. The motion of the electron will be along the line of the electric field vector.
Comparing the magnitudes of the forces: The force due to the electric field is \(F_E = eE\). Once the electron starts moving, it will also experience a magnetic force \(F_B = evB\). For an EM wave, the magnitudes of the fields are related by \(E = cB\), where \(c\) is the speed of light.
Thus, \(F_B = ev(E/c) = (v/c)F_E\). Since the velocity of the electron \(v\) will be much smaller than the speed of light \(c\) (\(v \ll c\)), the magnetic force \(F_B\) is significantly weaker than the electric force \(F_E\). The dominant force that governs the motion of the electron is the electric force.

Step 4: Final Answer:
The electron will primarily be driven by the electric field and will start moving along the direction of the electric field.